Background technology
The principle of work of metal resistance strain gauge is resistance strain effect, and namely tinsel is when being subject to effects of strain, and its resistance, along with the size of occurred mechanically deform (stretching or compression), corresponding change occurs.The theoretical formula of resistance strain effect is as follows:
Wherein R is its resistance value, and ρ is metal material resistivity, and L is metal material length, and S is metal material sectional area.Tinsel occurs in the process of mechanically deform bearing strain, and ρ, L, S will change, thus will inevitably cause the change of metal material resistance value.When metal material is stretched, length increases, and sectional area reduces, and resistance value increases; When by compression, length reduces, and sectional area increases, and resistance value reduces.Therefore, as long as the change of resistance value can be measured, just known strained situation wiry.Metal material resistance change rate formula can be derived by relevant knowledges such as formula (1) and the mechanics of materials
Wherein Δ R is resistance variation amount, and Δ L is the variable quantity of metal material length on pulling force or pressure action direction, and ε is that the strain on same direction is usually called axial strain, and K is metal material ga(u)ge factor.
In actual applications, metal resistance strain gauge is pasted onto the surface of Sensor Elastic Element or tested mechanical component.When the flexible member in sensor or tested mechanical component produce strain by acting force, also there is identical mechanically deform in the foil gauge pasted thereon thereupon, causes foil gauge resistance that corresponding change occurs.At this moment, mechanical quantity is just converted to the variable quantity output of resistance by resistance strain gage.
But we also need the partial derivative understanding workpiece strain sometimes, such as have six kinds of occasions below, but are not limited thereto six, need to use surface of the work strain partial derivative:
The first, concentrate owing to there will be strain near workpiece shapes sudden change place, often become workpiece and first occur damaging part, the strain partial derivative near sudden change place of monitoring shape, this place strain intensity can be obtained intuitively.
Second, exist in a large number by comer pieces in building, bridge, plant equipment, mechanics of materials relevant knowledge tells us, bent beam surface axial strain is directly proportional to section turn moment, the axial first-order partial derivative of section turn moment is directly proportional to cross section shearing strain, namely can know cross section shearing strain by the axial first-order partial derivative of surperficial axial strain, and this shearing strain directly cannot measure at surface of the work with foil gauge;
3rd, during applied elasticity research workpiece strain, internal strain is decided by partial differential equation, and equation solution needs boundary condition, and surface of the work strain partial derivative is exactly one of boundary condition, and this is that general foil gauge cannot provide.
In addition, to some position of workpiece, the such as position such as the shaft shoulder, part edge place, due to the sudden change of geomery, it strains the change that often corresponding existence is larger.But, just due to the sudden change of geomery, make the foil gauge that the more difficult arrangement in this place is general, need the product of a kind of energy inclined marginal position of monitor strain sheet instead of center position strain local derviation.
Summary of the invention
The deficiency of strain local derviation cannot be detected in order to overcome existing metal strain plate, the invention provides and a kind ofly can mix interdigital metal strain plate by the monitor strain bilateral measured that more effectively can detect the horizontal local derviation of the surface strain lateral deviation six sensitive grid full-bridge that is biased sensitive grid central cross local derviation, particularly there is the horizontal single order local derviation of size restriction site at measuring workpieces corner, edge etc. to foil gauge.
The technical solution adopted for the present invention to solve the technical problems is:
A kind ofly measure the lateral deviation six sensitive grid full-bridge that bilateral is biased sensitive grid central cross local derviation and mix interdigital metal strain plate, comprise substrate, described metal strain plate also comprises six sensitive grids, the two ends of each sensitive grid connect a pin respectively, described substrate are fixed described six sensitive grids;
Each sensitive grid comprises sensitive segment and transition section, the two ends of described sensitive segment are transition section, described sensitive segment is elongated strip shaped, described transition section is tubbiness shape, the resistance of described sensitive segment is much larger than the resistance of described transition section, under same strain state, the increased resistance value of described sensitive segment is much larger than the increased resistance value of described transition section, and the increased resistance value of described transition section is close to 0;
All xsect centres of form of each sensitive segment form sensitive segment axis, this sensitive segment axis is straight line section, in described six sensitive grids each sensitive segment axis being parallel and be arranged in same plane, sensitive segment axis is determined in plane, along described sensitive segment axis direction namely axially, be laterally with axially vertical direction; Each and with this sensitive segment resistance value for nominal mass is formed the nominal particle of place sensitive segment, the centroid position that the nominal particle of each sensitive segment is formed jointly is the center of sensitive grid;
, there is part deviation in the horizontal in six sensitive grid center bias frees in the axial direction; The order of sensitive grid center pressed by each sensitive grid, and transversely from top to bottom, being first upper three sensitive grids and a upper sensitive grid, is then middle first sensitive grid and middle second sensitive grid, is finally next sensitive grid and lower three sensitive grids; The spacing at upper three sensitive grid centers and a upper sensitive grid center is 0, and the spacing at upper three sensitive grid centers and middle first sensitive grid center is Δ y
1, the distance at middle first sensitive grid center and middle second sensitive grid center is 0, and the spacing at middle first sensitive grid center and next sensitive grid center is also Δ y
1the spacing at next sensitive grid center and lower three sensitive grid centers is 0, each sensitive segment axis is determined in plane, upper three sensitive grids, a upper sensitive grid, between middle first sensitive grid and middle second sensitive grid mutually in interdigital layout, next sensitive grid, lower three sensitive grids, between middle first sensitive grid and middle second sensitive grid mutually in interdigital layout;
The sensitive segment all-in resistance of upper three sensitive grids, a upper sensitive grid, middle first sensitive grid, middle second sensitive grid, next sensitive grid and lower three sensitive grids is the proportionate relationship of 3:1:4:4:1:3, and upper three sensitive grids, a upper sensitive grid, middle first sensitive grid, middle second sensitive grid, next sensitive grid and the all-in resistance changing value of sensitive segment sensitive segment under identical strain of lower three sensitive grids are also the proportionate relationship of 3:1:4:4:1:3.
Accordingly, upper three sensitive grids of series connection and next sensitive grid, middle first sensitive grid, the upper sensitive grid of series connection and lower three sensitive grids, middle second sensitive grid just in time form four brachium pontis of measuring bridge.
Further, all shape of cross section consistent size of each sensitive segment, get the axis point midway of each sensitive segment and with this sensitive segment resistance value for nominal mass is formed the nominal particle of place sensitive segment, the sensitive segment total length of described upper three sensitive grids, a upper sensitive grid, middle first sensitive grid, middle second sensitive grid, next sensitive grid and lower three sensitive grids is the proportionate relationship of 3:1:4:4:1:3.The program is a kind of scheme that can select, as long as the position of nominal particle meets the equal xsect position of form center of its both sides resistance value, also can be other positions.
Further, upper three sensitive grids, a upper sensitive grid, between next sensitive grid and lower three sensitive grids mutually in interdigital layout, certainly, also can be non-interdigital layout; Described interdigital layout refers to: in the plane, in the sensitive segment distribution straggly with two sensitive grids on sensitive segment axes normal direction, the order occur respectively the sensitive segment of two sensitive grids in the direction in which and number of times do not limit in each sensitive segment axis institute of two sensitive grids.
Utilize the linear relationship between metal material increased resistance value and strain, this foil gauge may be used for monitor strain as common foil gauge.On the other hand, according to (" numerical computation method " 21 pages (1.4.11)-(1.4.14) formula as Yi Fengkang etc. compiles, National Defense Industry Press publishes in Dec, 1978 makes equidistant interpolation analysis) in numerical differentiation theory about the circular of single order local derviation, the numerical computation method of the y direction first-order partial derivative of f (x, y) is as follows:
Wherein y
1=y
0+ h, y
2=y
1+ h, paying special attention to above formula is (x, y
2) the first-order partial derivative value formula of position, the truncation error of this formula is less is o (h
2) be the higher order indefinite small of step-length square.By the strain that formula (2) engineering be it is generally acknowledged sensitive grid resistance change direct ratio and sensitive grid center, in conjunction with the proportionate relationship of each sensitive grid resistance and the resistance change under same strain, resistance and the resistance value deducting middle first sensitive grid of upper three sensitive grids and next sensitive grid, again except the distance at above three sensitive grid centers and next sensitive grid center is the horizontal single order numerical value local derviation strained, according to numerical differentiation theory, this is the single order numerical value local derviation of upper three sensitive grid centers, and this is not in the middle part of foil gauge but the horizontal single order local derviation in portion on the upper side; Equally, resistance and the resistance value deducting middle second sensitive grid of lower three sensitive grids and a upper sensitive grid, again except the distance at following three sensitive grid centers and a upper sensitive grid center is the horizontal single order numerical value local derviation strained, the horizontal single order numerical value local derviation of lower three sensitive grid centers according to theoretical this of numerical differentiation, neither in the middle part of foil gauge but the horizontal single order local derviation in portion on the lower side.Therefore the advantage of this foil gauge is that its upper and lower both sides all can limit the horizontal single order local derviation at the position that cannot measure due to size by the general foil gauge such as measuring workpieces corner, edge.
Technique should be noted keep three sensitive grids, on a sensitive grid, middle first sensitive grid, middle second sensitive grid, next sensitive grid and lower three sensitive grid transition section all-in resistances and the variable quantity of transition section resistance under external strain be that the proportionate relationship of 3:1:4:4:1:3 is to heighten measuring accuracy, if the resistance of transition section and the lower resistance change of strain be can not ignore, also can be eliminated when detecting as systematic error.
Further, described metal strain plate also comprises cover plate, and described cover plate is covered in described sensitive grid and substrate.
Further again, described sensitive grid is wire form, foil, diaphragm type or thick-film type sensitive grid.
Further, described substrate is glued membrane substrate, glass fabric substrates, asbestos substrate, metallic substrates or temporary substrate.
Described six sensitive grid upper, middle and lower are arranged in substrate.Certainly, also can be other arrangement.
Beneficial effect of the present invention is mainly manifested in: all can there be the horizontal single order local derviation of size restriction site the upper and lower both sides that foil gauge effectively can detect surface strain transverse direction the single order local derviation, particularly foil gauge of upper three sensitive grid centers and lower three Liang Ge positions, sensitive grid center simultaneously in measuring workpieces corner, edge etc. to foil gauge.
Embodiment
Below in conjunction with accompanying drawing, the invention will be further described.
With reference to Fig. 1 ~ Fig. 3, a kind ofly measure the lateral deviation six sensitive grid full-bridge that bilateral is biased sensitive grid central cross local derviation and mix interdigital metal strain plate, comprise substrate, described metal strain plate also comprises six sensitive grids, the two ends of each sensitive grid connect a pin respectively, described substrate are fixed described six sensitive grids;
Each sensitive grid comprises sensitive segment and transition section, the two ends of described sensitive segment are transition section, described sensitive segment is elongated strip shaped, described transition section is tubbiness shape, the resistance of described sensitive segment is much larger than the resistance of described transition section, under same strain state, the increased resistance value of described sensitive segment is much larger than the increased resistance value of described transition section, and the increased resistance value of described transition section is close to 0;
All xsect centres of form of each sensitive segment form sensitive segment axis, this sensitive segment axis is straight line section, in described six sensitive grids each sensitive segment axis being parallel and be arranged in same plane, sensitive segment axis is determined in plane, along described sensitive segment axis direction namely axially, be laterally with axially vertical direction; Each sensitive segment exists the xsect that its both sides resistance value is equal, get this cross-section centroid position and with this sensitive segment resistance value for nominal mass is formed the nominal particle of place sensitive segment, the centroid position that the nominal particle of each sensitive segment is formed jointly is the center of sensitive grid;
, there is part deviation in the horizontal in six sensitive grid center bias frees in the axial direction; The order of sensitive grid center pressed by each sensitive grid, and transversely from top to bottom, being first upper three sensitive grids and a upper sensitive grid, is then middle first sensitive grid and middle second sensitive grid, is finally next sensitive grid and lower three sensitive grids; The spacing at upper three sensitive grid centers and a upper sensitive grid center is 0, and the spacing at upper three sensitive grid centers and middle first sensitive grid center is Δ y
1, the distance at middle first sensitive grid center and middle second sensitive grid center is 0, and the spacing at middle first sensitive grid center and next sensitive grid center is also Δ y
1the spacing at next sensitive grid center and lower three sensitive grid centers is 0, each sensitive segment axis is determined in plane, upper three sensitive grids, a upper sensitive grid, between middle first sensitive grid and middle second sensitive grid mutually in interdigital layout, next sensitive grid, lower three sensitive grids, between middle first sensitive grid and middle second sensitive grid mutually in interdigital layout;
The sensitive segment all-in resistance of upper three sensitive grids, a upper sensitive grid, middle first sensitive grid, middle second sensitive grid, next sensitive grid and lower three sensitive grids is the proportionate relationship of 3:1:4:4:1:3, and upper three sensitive grids, a upper sensitive grid, middle first sensitive grid, middle second sensitive grid, next sensitive grid and the all-in resistance changing value of sensitive segment sensitive segment under identical strain of lower three sensitive grids are also the proportionate relationship of 3:1:4:4:1:3.
Accordingly, upper three sensitive grids of series connection and next sensitive grid, middle first sensitive grid, the upper sensitive grid of series connection and lower three sensitive grids, middle second sensitive grid just in time form four brachium pontis of measuring bridge.
Further, all shape of cross section consistent size of each sensitive segment, get the axis point midway of each sensitive segment and with this sensitive segment resistance value for nominal mass is formed the nominal particle of place sensitive segment, the sensitive segment total length of described upper three sensitive grids, a upper sensitive grid, middle first sensitive grid, middle second sensitive grid, next sensitive grid and lower three sensitive grids is the proportionate relationship of 3:1:4:4:1:3.The program is a kind of scheme that can select, as long as the position of nominal particle meets the equal xsect position of form center of its both sides resistance value, also can be other positions.
Further, upper three sensitive grids, a upper sensitive grid, next sensitive grid and lower three sensitive grids, mutually in interdigital layout, certainly, also can be non-interdigital layout; Described interdigital layout refers to: in the plane, in the sensitive segment distribution straggly with two sensitive grids on sensitive segment axes normal direction, the order occur respectively the sensitive segment of two sensitive grids in the direction in which and number of times do not limit in each sensitive segment axis institute of two sensitive grids.
The lateral deviation six sensitive grid full-bridge that the bilateral measured of the present embodiment is biased sensitive grid central cross local derviation mixes interdigital metal strain plate, comprise substrate 1, described metal strain plate also comprises six sensitive grids, the two ends of each sensitive grid connect a pin respectively, described substrate 1 are fixed described six sensitive grids.
Three sensitive grids 2, a upper sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5, next sensitive grid 6 and lower three sensitive grids 7 can be fixed on substrate 1, for keep each sensitive grid fixing shape, position and size; Substrate 1 is very thin, thus the strain of surface of test piece is delivered to exactly upper three sensitive grids 2, a upper sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5, next sensitive grid 6 and lower three sensitive grids 7.Substrate 1 can be glued membrane substrate, glass fabric substrates, asbestos substrate, metallic substrates and temporary substrate.Usually with cohering, weld, substrate is fixed on the tested position of test block by the mode such as ceramic spraying.Substrate 1 also can be printed on the lines that some are located for foil gauge.
The materials such as cover plate paper using or glue are made, and are covered in three sensitive grids 2, a upper sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5, next sensitive grid 6, lower three sensitive grids 7 and substrate 1, play the protective seam of the effects such as protection against the tide, corrosion protection, loss prevention.
Pin 8 is for connecting sensitive grid and metering circuit, upper three sensitive grids 2, a upper sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5, next sensitive grid 6 and lower three sensitive grids 7 respectively have two pins 8, to with foil and membrane type foil gauge, upper three sensitive grids 2 that pin 8 is connected with it, a upper sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5, next sensitive grid 6 and lower three sensitive grids 7 combine as a whole.Two pins of upper three sensitive grids 2 are 8-1 and 8-2, two pins of a upper sensitive grid 3 are 8-3 and 8-4, two pins of middle first sensitive grid 4 are 8-5 and 8-6, two pins of middle second sensitive grid 5 are 8-7 and 8-8, two pins of next sensitive grid 6 are 8-9 and 8-10, and two pins of lower three sensitive grids 7 are 8-11 and 8-12.
Upper three sensitive grids 2, a upper sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5, next sensitive grid 6 and lower three sensitive grids 7, according to the difference of its metal sensitive material and processing technology, can be wire form, foil, diaphragm type, thick-film type.No matter the thickness of which kind of upper three sensitive grid 2, a upper sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5, next sensitive grid 6 and lower three sensitive grids 7 is all very little, make the axial length of three sensitive grids 2, a upper sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5, next sensitive grid 6 and time three sensitive grids 7 with it depend on the deformation of workpiece and change.The basic crucial part of the present invention is three sensitive grids 2, a upper sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5, cooperation between next sensitive grid 6 and lower three sensitive grids 7, has following main points:
The first, six sensitive grids are arranged in substrate, is called three sensitive grids 2, a upper sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5, next sensitive grid 6 and lower three sensitive grids 7.
The second, upper three sensitive grids 2, a upper sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5, next sensitive grid 6 and lower three sensitive grids 7 all can be divided into sensitive segment 9 and transition section 10, and each sensitive segment 9 is connected to form sensitive grid by each transition section 10.Comparatively speaking, sensitive segment 9 is in elongated shape, and resistance is comparatively large and its resistance is comparatively responsive to strain; Described transition section 10, substantially in tubbiness shape, makes the resistance of described transition section very little and insensitive to strain, and under duty, resistance variations is close to 0, and therefore the summation of sensitive segment resistance is the all-in resistance of single sensitive grid substantially.Fig. 2 has marked sensitive segment 9 and transition section 10 in more detail from angle more clearly.
3rd, the sensitive segment of each sensitive grid 9 is in elongated strip, and all xsect centres of form of each sensitive segment 9 form sensitive segment axis, and this sensitive segment 9 axis is straight line section, the axis being parallel of each sensitive segment 9 and be arranged in same plane.All xsects of each sensitive segment 9 are consistent along the projection of shape of sensitive segment axis direction.Get the axis point midway of each sensitive segment and with this sensitive segment resistance value for nominal mass is formed the nominal particle of place sensitive segment, the centroid position that the nominal particle of each sensitive segment is formed jointly is the center of sensitive grid.
4th, upper three sensitive grids 2, a upper sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5, sensitive segment 9 total length of next sensitive grid 6 and lower three sensitive grids 7 is the proportionate relationship of 3:1:4:4:1:3, upper three sensitive grids 2, a upper sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5, sensitive segment 9 all-in resistance of next sensitive grid 6 and lower three sensitive grids 7 is the proportionate relationship of 3:1:4:4:1:3, upper three sensitive grids 2, a upper sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5, next sensitive grid 6 and the all-in resistance changing value of sensitive segment 9 sensitive segment under identical strain of lower three sensitive grids 7 are also the proportionate relationship of 3:1:4:4:1:3.Accordingly, upper three sensitive grids 2 of series connection and next sensitive grid 6, middle first sensitive grid 4, the upper sensitive grid 3 of series connection and lower three sensitive grids 7, middle second sensitive grid 5 just in time form four brachium pontis of measuring bridge.
5th, overlook three sensitive grids 2, a upper sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5, next sensitive grid 6 and lower three sensitive grids 7, they all have axis of symmetry and axis of symmetry overlaps (y-axis in Fig. 2), upper three sensitive grids 2, a upper sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5, next sensitive grid 6 sensitive segment 9 respective with lower three sensitive grids 7 is all vertical with this axis of symmetry, and the sensitive segment 9 of each sensitive grid all distributes about this rotational symmetry.Therefore, can say three sensitive grids 2, a upper sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5, next sensitive grid 6 and lower three sensitive grid 7 centers all in y-axis, there is part deviation in their center bias free in the axial direction in the horizontal.According to the vertical view of foil gauge in Fig. 2, the sensitive segment 9 of upper three sensitive grids 2 and a upper sensitive grid 3 has axial axis of symmetry x
u, the center of upper three sensitive grids 2 and a upper sensitive grid 3 is at y-axis and x
uthe intersection point of axle, the sensitive segment 9 of middle first sensitive grid 4 and middle second sensitive grid 5 has axial axis of symmetry x, and the center of middle first sensitive grid 4 and middle second sensitive grid 5 is at the intersection point of y-axis and x-axis, and the sensitive segment 9 of next sensitive grid 6 and lower three sensitive grids 7 has axial axis of symmetry x
l, the center of next sensitive grid 6 and lower three sensitive grids 7 is at y-axis and x
lthe intersection point of axle.
6th, the spacing at the center of upper three sensitive grids 2 and the center of a upper sensitive grid 3 is 0, and the spacing at the center of upper three sensitive grids 2 and the center of middle first sensitive grid 4 is Δ y
1, the distance at the center of middle first sensitive grid 4 and the center of middle second sensitive grid 5 is 0, and the spacing at the center of middle first sensitive grid 4 and the center of next sensitive grid 6 is also Δ y
1, the spacing at the center of next sensitive grid 6 and the center of lower three sensitive grids 7 is 0, as shown in Figure 2.Each sensitive segment axis is determined in plane, upper three sensitive grids 2, a upper sensitive grid 3, middle first sensitive grid 4 and middle second sensitive grid 5 is in interdigital layout, next sensitive grid 6, lower three sensitive grids 7, middle first sensitive grid 4 and middle second sensitive grid 5 are in interdigital layout, and upper three sensitive grids 2, a upper sensitive grid 3, next sensitive grid 6, lower three sensitive grids 7 can be interdigital layout or non-interdigital layout; Described interdigital layout refers to: in the plane, in the sensitive segment distribution straggly with two sensitive grids on sensitive segment axes normal direction, the order occur respectively the sensitive segment of two sensitive grids in the direction in which and number of times do not limit in each sensitive segment axis institute of two sensitive grids.Because the relative position of upper three sensitive grids 2, a upper sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5, next sensitive grid 6 and lower three sensitive grids 7 is ensured quite accurately to be secured by foil gauge production technology, this is also that the present invention can detect workpiece and strains one of key of horizontal partial derivative.
In sum, in the present invention, three sensitive grids 2, a upper sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5, next sensitive grid 6 and lower three sensitive grids 7 increased resistance value under same strain are the proportionate relationship of 3:1:4:4:1:3; , there is part deviation in the horizontal in each sensitive grid center bias free in the axial direction; The spacing at the center of upper three sensitive grids 2 and the center of a upper sensitive grid 3 is 0, and the spacing at the center of upper three sensitive grids 2 and the center of middle first sensitive grid 4 is Δ y
1, the distance at the center of middle first sensitive grid 4 and the center of middle second sensitive grid 5 is 0, and the spacing at the center of middle first sensitive grid 4 and the center of next sensitive grid 6 is also Δ y
1, the spacing at the center of next sensitive grid 6 and the center of lower three sensitive grids 7 is 0.
Under making free state, upper sensitive grid 3 resistance is R
u0, middle second sensitive grid 5 resistance is R
m0, lower three sensitive grid 7 resistance are R
l0, should R be had
u0+ R
l0=R
m0=R
0.Foil gauge of the present invention is placed in certain when having a surface strain, upper sensitive grid 3 resistance is R
0+ Δ R
u, middle second sensitive grid 5 resistance is R
0+ Δ R
m, lower three sensitive grid 7 resistance are R
0+ Δ R
l; On the other hand, the center of a upper sensitive grid 3 and lower three sensitive grids 7 is in the horizontal at a distance of 2 Δ y
1.The formula of the relation of sensitive grid resistance and surface strain and numerical differentiation (3) is utilized to have:
Wherein
for the center of lower three sensitive grids 7, ε
ufor the strain of upper sensitive grid 3 center, ε
mfor the strain of middle second sensitive grid 5 center, ε
lfor the strain of lower three sensitive grid 6 centers.Namely this is the principle that the present embodiment measured surface strains horizontal local derviation.Pay special attention to, the numerical differentiation that above formula calculates is the horizontal single order local derviation of strain of the center of lower three sensitive grids 7, this position is the downside of foil gauge, therefore has and is convenient to there are the horizontal single order local derviation of size restriction site in measuring workpieces corner, edge etc. advantage to foil gauge.Three sensitive grids 2, middle first sensitive grid 4 and next sensitive grid 6 in same utilization, also can measure the horizontal single order local derviation of strain of the center of three sensitive grids 2.The horizontal single order local derviation of strain of the center of above-mentioned lower three sensitive grids 7 and the horizontal first-order partial derivative of strain of upper three sensitive grid 2 centers can be measured simultaneously.
Coordinated by the present embodiment electric bridge to can be used for monitor strain, strain horizontal single order local derviation, suppose that bridge input voltage is u
i, output voltage is u
o, Fig. 3 is shown in by the schematic diagram of measuring bridge.When without workpiece effects of strain, each arm resistance of electric bridge is labeled as R respectively according to clockwise direction
1, R
2, R
3, R
4, when obscuring also with these sign flag resistance place electric bridges.Each electric bridge can be laid sensitive grid or the resistance of foil gauge.Arrange identical with general foil gauge, if settle sensitive grid on multiple brachium pontis, to the order of each installation position, the requirement of strain difinite quality.During without workpiece effects of strain, the Output Voltage Formula of electric bridge is
Now, bridge balance i.e. u is required
o=0, so so-called bridge balance condition R must be met
1r
3-R
2r
4=0, the electric bridge of employing meets further
R
1=R
2=R
3=R
4,(6)
Because, the first, satisfy condition (6) time, the highest according to relevant theoretical foil gauge sensitivity; The second, monitor strain or strain horizontal local derviation the equal requirement condition of method (6) set up.When foil gauge, with external world's strain, strain also occurs, above-mentioned bridge balance condition is generally no longer set up, now
Due to Δ R
i< < R
i(i=1,2,3,4) event first ≈ sets up, and second ≈ is as Δ R
1-Δ R
2with Δ R
3-Δ R
4jack per line or contrary sign but | Δ R
1-Δ R
2| with | Δ R
3-Δ R
4| not very close to time set up, in engineering, choose reasonable foil gauge installation position can realize completely.The voltage measurement strain that general available formula (7) obtains; Can convolution (4) and formula (7) to the horizontal local derviation of strain, reasonable design arranges each brachium pontis sensitive grid and resistance, such as brachium pontis R
1second sensitive grid 5 in layout, brachium pontis R
2a sensitive grid 3 and lower three sensitive grids 7 in arranged in series, all the other brachium pontis configuration substitutional resistance, can obtain and strain the linear magnitude of voltage u of horizontal single order local derviation with lower three sensitive grid 7 centers
o, this voltage is that feeble signal need be amplified.